It seems intuitively clear to me that ST would soon reach a point at which additional increments -- even considered in isolation -- are not worth it.
For example, if one hundred equal increments yielding 100x pain for $100y are collectively not worth it, then the badness of 100x pain outweighs the value of $100y. On average, then, the harm of x outweighs the benefit of y, over the 100 increments. If the increments are all of equal net value, then each increment is of negative net value, and hence irrational to choose. If instead we allow that the first few increments were worth the money (due perhaps to the diminishing marginal utility of money, or else the increasing marginal disutility of pain) then we can at least know that the one hundredth increment is not worth taking. After 99 increments, the value of $y is outweighed by the badness of x pain. It would be incoherent to deny this while holding that the value of $100y is outweighed by the badness of 100x pain. So there's no real puzzle here.
But, strangely, Tenenbaum and Raffman, in 'Vague Projects and the Puzzle of the Self-Torturer', do deny this. They instead affirm (p.98):
Nonsegmentation: When faced with a certain series of choices, the rational self-torturer must choose to stop turning the dial before the last setting; whereas in any isolated choice, she must (or at least may) choose to turn the dial.
Why do they think this? They seem to assume that our interest in avoiding pain is vague and coarse-grained. They refer to "our commitment to a project of leading a (relatively) pain free life" (p.107). Since a negligible increase in pain cannot make a difference to whether or not we live a relatively pain-free life, no individual increment violates this interest of ours,* whereas each increment does serve our interest in greater wealth. (If you're already in pain, I imagine that T&R might appeal to some other coarse-grained anti-pain interest, just with higher thresholds, such as that of leading a life that is not excessively inundated with pain.)
There are (at least) two obvious problems here. One, noted by Luke Elson in his reply, is that the asterisked claim above is false. In a sorites series like this, it is not universally true that each increment determinately makes no difference to whether the vague predicate applies. Rather, on standard views of vagueness (e.g. supervaluationism), there will be a range in which it is indeterminate which particular increment violates the threshold, but determinate that some such increment does. It is thus (determinately) false to claim that no increment violates our interest in leading a relatively pain-free life.
Secondly, and more fundamentally, it just seems absurd to me to think that our interests in avoiding pain are coarse-grained in this way. What's so special about the borderline between a life that is "relatively" pain free and one that is not? Suppose it takes 20 increments of pain to reach the borderline cases, which in turn extend for 5 increments before we reach the realm in which you determinately no longer qualify as leading a "relatively pain-free life". Are we supposed to imagine that a rational person could prefer to increase from 0 to 19 points of pain than to increase from 19 to 25? Are the latter 6 points intrinsically more significant because they happen to span the boundaries of the English language predicate "is a relatively pain-free life"? C'mon. Pain is pain. It doesn't matter what we call it. We may use various vague and coarse-grained categorizations for ease of description, but it is ridiculous to think that it's these categorizations rather than the underlying level of pain that we fundamentally care about!
So it seems to me that T&R are making the mistake diagnosed in my old post on Apparent Vagueness and Graded Harms. Just because we use vague language to categorize some of the things in the world that we care about (be it pain or pollution), it doesn't follow that the underlying phenomenon that we care about is vague. Indeed, once the contrast is made clear, it would seem positively irrational to care about the vague categorizations rather than the underlying spectrum.
Am I missing something?
[See also my follow-up post: Self-Torturers without Diminishing Marginal Value.]